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A079937
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Greedy frac multiples of Pi^2/6: a(1)=1, Sum_{n>=1} frac(a(n)*x) = 1 at x = Pi^2/6.
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5
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1, 2, 14, 45, 107, 138, 276, 414, 1135, 2270, 6672, 12209, 18881, 180865
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OFFSET
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1,2
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COMMENTS
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The n-th greedy frac multiple of x is the smallest integer that does not cause Sum_{k=1..n} frac(a(k)*x) to exceed unity; an infinite number of terms appear as the denominators of the convergents to the continued fraction of x.
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LINKS
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EXAMPLE
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a(4) = 45 since frac(1*x) + frac(2*x) + frac(14*x) + frac(45*x) < 1, while frac(1*x) + frac(2*x) + frac(14*x) + frac(k*x) > 1 for all k > 14 and k < 45.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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